Baby Donald was actually Cary Darling, a 50-year-old father of two working for tips to support his family. It could be risky. While most Trump supporters were friendly, one spat in his face and another harassed him and urged him to hang himself.

Then there was the time a tourist mistook Mr. Darling’s character for a political promotion and, after cursing Mr. Trump, punched him in the face.

“This is a really weird election,” Mr. Darling said.

America’s political divides can be felt even in the country’s sin city, the desert oasis where dazzle and extravagance are a way of life. In a sense, it was Las Vegas’s proud reputation for lurid excess, for being a place where almost anything goes, that seemed to make it the perfect backdrop for the third and final American presidential debate, which took place here on Wednesday night.

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Las Vegas proved to be an apt host for the debate, part of America’s extravagant process of choosing a president.CreditDeclan Walsh/The New York Times

The debate had none of the splashy excess of the casino mega-resorts a few miles away, along the city’s million-watt main strip, where one hotel is shaped like an Egyptian pyramid and there is a bewildering choice of shows featuring famous magicians, singers, circus acts and strippers.

Yet, in its own way, the event was an apt reflection of America’s elaborate process of choosing a president — an exhausting, 18-month marathon of elections, debates and TV-driven rituals costing hundreds of millions of dollars, now grinding toward its climax with the vote on Nov. 8.

The Las Vegas debate cost $8 million to put on and was almost a year in the making, said Valarie Segerra, one of the organizers. The stage had been trucked 2,500 miles across the country to the venue on the University of Nevada, Las Vegas, campus. Organizers erected three miles of fencing and strategically placed 190 shipping containers to guard against terrorist attacks. Power and internet backup systems had to be provided; 1,000 student volunteers were recruited to guide visitors.

The giant arena that hosted the debate had previously held major boxing matches and rodeo competitions. The Commission for Presidential Debates, the nonprofit group that organized the debates, used giant black drapes to set aside a section for this encounter, and it set specific requirements for the climate inside: The temperature had to hover between 63 and 65 degrees, and the humidity had to be less than 50 percent.

The debates commission, which has organized every debate since 1988, calibrates every aspect to ensure parity. The same stage used in the first two debates was used in Las Vegas. Anything that could provide a perceived advantage — who stands left or right on the stage, who walks out first, whether they shake hands — was previously decided with the candidates through consensus or a coin toss, said Peter Eyre, a commission spokesman.

“We want them to be as equal as possible,” he said.

He declined to comment on the controversy that erupted at the previous debate, in St. Louis, when Mr. Trump tried to bring three women who had accused Hillary Clinton’s husband, former President Bill Clinton, of sexual misconduct, into the V.I.P. box.

The debates, political theater writ large, are part of a proud American tradition that stretches back to 1858, when Abraham Lincoln and Stephen Douglas argued over slavery during a race for a Senate seat from Illinois.

With 150,000 hotel rooms and an array of cavernous conference halls, Las Vegas was well equipped to accommodate the thousands of journalists who descended on the city, although it had never previously hosted a presidential debate, or indeed, any national political event. Mr. Trump owns 50 percent of a shimmering gold hotel here, now at the heart of a heated labor dispute. (He refuses to recognize the powerful Culinary Workers Union, which is campaigning for Mrs. Clinton in the election).

After a grinding campaign season, some reporters made the most of the city’s attractions. The team from Fox News set up a studio on the rooftop of the MGM Grand, overlooking the strip. On the eve of the debate, the anchor Steve Doocy celebrated his birthday alongside a group of tiara-wearing choral singers. Nearby another reporter was filmed twirling in the pool, still wearing his shirt and tie, surrounded by synchronized swimmers. “I saw him drinking beer a minute ago,” Mr. Doocy said. “Next thing you know he’s in an inner tube with these ladies.”

In all, over 5,000 journalists traveled to Las Vegas for the debate. They clustered in studios, set up live positions and gathered in a giant hall. CNN alone had set up three temporary studios, erected six other interview positions and deployed at least 30 cameras.

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Over 5,000 journalists traveled to Las Vegas for the debate.CreditDeclan Walsh/The New York Times

On Wednesday, four hours before the debate started, guests and anchors cycled on and off an outdoor stage on the college campus with an air of practiced familiarity.

Behind the TV set was another scene that has become a ritual of political elections: dozens of supporters of the candidates holding aloft giant signs, jostling to be seen in the background of the TV shot. Clinton supporters wore pink T-shirts for Planned Parenthood. As the studio guests talked, Trump supporters yelled, “CNN for Donald Trump,” a sarcastic reference to the network, which has been derided by Mr. Trump as the Clinton News Network.

When the debate started hours later, at 6 p.m., journalists crowded into a vast hall to write, comment and talk about the event, which had the air of a keenly anticipated theatrical performance. In the press center, 50 televisions hung from the roof, relaying the proceedings.

A hush fell over the hall during the debate The silence was broken just a few times, usually when one of the candidates let rip a zinger, like Mr. Trump’s reference to illegal immigrants as “bad hombres,” or Mrs. Clinton’s taunts about his hotel.

Yet at the end, instead of applause, there was silence. For once in Vegas, a performance had ended without a reaction.

More important was the reaction of the roughly 70 million Americans watching across the country. Mr. Darling, the Baby Trump, was not among them. Avoiding the debate parties, he stayed home to watch a movie with his sons. He couldn’t wait for the vote on Nov. 8, he said Thursday, “so all of this will finally be over.”

Correction:

Because of editing errors, an earlier version of a picture caption with this article misstated the given name of the man pictured and misidentified the casino he was standing in front of. He is Cary Darling, not Carl, and he was at the Fremont Hotel and Casino, not the Four Queens Hotel and Casino.

Correction:

An earlier version of this article misstated the motto on Cary Darling’s T-shirt. It says “Make my diaper great again,” not “Make diapers great again.”